A mini-refrigeration system consisting of heat exchanger, expansion nozzle and condensation chamber is shown in FIG. 28 of "Silicon as a Mechanical Material", K.E. Petersen, Proceedings of the IEEE, Vol.70, No.5, May 1982, page 435-436. This cooling system is micro-mechanically made of silicon and works like a Joule-Thomson Cooler with single-acting throttling, as described in "Kryotechnik", W. G. Fastowski et al., page 106, Abb. 34. The cooling system allows the liquefication of nitrogen at a pressure of more than 100 bar.
Because Joule-Thomson Coolers work effectively only at temperatures below 200K and/or at high pressure (higher than 75 bar), commercial low-temperature machines use the adiabatic-isothermic expansion cycle discussed in "Kryotechnik", W.G.Fastowski et al., chapter 3.9.1., page 175. While expanding, a compressed gas executes external work without heat energy being supplied or carried off. This external work has to be dissipated, e.g., in form of mechanical or electrical energy, to regions outside of the "cold zone" of the device.
Normally, the expanding working gas drives an expansion turbine, as shown for helium in "Kryotechnik", W.G. Fastowski et al., chapter 3.8., page 173. Expansion machines consisting of pistons, clack valves, paddle wheels and the like tend to be relatively expensive or may not be implemented in a miniature refrigeration system.
In "Temperature Separation Produced By A Hartmann-Sprenger Tube Coupling A Secondary Resonator", International Journal of Heat Mass Transfer, Vol. 24, No. 12, pp. 1951-1958, the use of a resonance tube (the Hartmann Sprenger tube) for temperature separation is described. A gas column driven by jet flow is excited to a finite amplitude oscillation by accompanying travelling shock waves. Compressed gas issuing from a nozzle and entering into the Hartmann Sprenger tube is separated into cold gas exhausted from the open end of the tube and hot gas discharged through a tiny orifice bored at the end wall of the tube. By coupling a secondary resonator to the resonance tube, the thermal effect can be improved.